We are interested in studying a physical model for a many-body system where the main contribution of the interaction of its constituents is pairwise and radial in nature. In addition, the physical conditions of the system (temperature, density, etc) are such, that its quantum behavior is non-negligible. In this section we set shortly the theoretical background, in order to establish our physical model with a central potential, and also the notation to be applied in the rest of the paper [1]}. The Hamiltonian for a system of two spinless particles with masses \(m_{1}\)  and \(m_{2}\)  interacting via a radial potential \(V\left( \left|\vec{r}_{1}-\vec{r}_{2}\right|\right) \)  is given by
\(H=T+V=\frac{p_{1}^{2}}{2m_{1}}+\frac{p_{2}^{2}}{2m_{2}}+V(\vert \vec{r}_{1}-\vec{r}_{2}\vert ). \) 
